If f(x)=2x(sinx+cosx)\displaystyle {f{{\left({x}\right)}}}={2}{x}{\left({\sin{{x}}}+{\cos{{x}}}\right)}, find f(x)\displaystyle {f}'{\left({x}\right)}.

f(x)\displaystyle {f}'{\left({x}\right)} =  

Evaluate the derivative at x=\displaystyle {x}=4. Enter an approximation, rounded to the nearest thousandth.

f(4)\displaystyle {f}'{\left({4}\right)} =